WASHINGTON (CNN) -- An unlikely pair of Senate allies called for a larger military Sunday and pledged a thorough investigation of abuse against Iraqi prisoners in Baghdad.

Sens. Hillary Rodham Clinton, D-New York, and Lindsey Graham, R-South Carolina, are both members of the Senate's Armed Services Committee.

"A number of us have been sounding this alarm. We have to face the fact we need a larger active-duty military," Clinton told the television show "Fox News Sunday."

"We cannot continue to stretch our troops, both active-duty, Guard and Reserve, to the breaking point, which is what we're doing now."

Graham said the United States is "putting too much pressure on the men and women in uniform."

"We need more of them, sooner rather than later," he said.

The senators acknowledged that an increase in the size of the military would be an expensive venture.

Clinton said, "I don't think we have any alternatives." And Graham said, "If we lose Iraq -- if it fails to go from a dictatorship to a democracy -- then we've had a great setback in the Mideast."

Recently published photographs depicting U.S. soldiers abusing Iraqi prisoners don't help matters, the senators said, and both said the investigation into the scandal would continue.

Graham said he believed the investigation would eventually reveal that more than the privates and sergeants currently charged were involved and that military intelligence officers directed some of the abuse.

He said he thought the investigation also would show that some soldiers did what they did on their own and that "it was the worst-run command situation I've ever seen."

"I think you're going to find a sophisticated plan that was in [place at the U.S. detention facility at Guantanamo Bay,] Cuba, about how to interrogate al Qaeda people was translated to an unsophisticated group in Iraq [that] was poorly trained, understaffed, and that the result was a cocktail for disaster," said Graham, an Air Force Reserve colonel.

He predicted there would be more courts-martial involving soldiers farther up the chain of command.

Graham and Clinton both appealed for an end to partisan wrangling so that the problems that created the Abu Ghraib scandal -- too few troops, and those being poorly trained and unprepared, along with a breakdown of command -- can be fixed.

"We are the greatest nation in the history of the world," Clinton said. "We have rule of law. We have due process. We have ideals and values. And, frankly, that's what we think we're fighting for. It is imperative that we do this right and that we follow the investigations wherever they lead."

"I would ask both sides to kind of knock it down a notch, work together to find more troops. If we can work together," Graham said, referring to himself and Clinton, "that's a good sign."

The former first lady was making her first appearance on "Fox News Sunday," and host Chris Wallace pointed out that she was appearing with Graham -- who was one of the "managers" from the House of Representatives who unsuccessfully prosecuted her husband's impeachment in his Senate trial.

"I don't think that was lost on her," Graham commented wryly.

Clinton said she believes "in redemption and growth."

"People who were previously misguided can see the light," she said.

Clinton said she and Graham had found "common cause" on several issues, particularly in their drive to grant the same health care benefits to National Guard and Reserve forces now provided to active-duty military.

"We have polar opposite views on a lot of things," Graham said. "But we're not going to win this war if we focus on what divides us. We need to focus on what brings us together.

"The men and woman who serve us are not Republicans or Democrats," he said. "They're Americans."